Analysis of the one dimensional inhomogeneous Jellium model with the Birkhoff-Hopf Theorem

TL;DR

This paper applies the Birkhoff-Hopf Theorem and Hilbert cone distances to establish decay of correlations, analyticity, and a central limit theorem in a one-dimensional inhomogeneous Jellium model for both classical and quantum cases.

Contribution

It introduces a novel application of the Birkhoff-Hopf Theorem to analyze inhomogeneous Jellium models, demonstrating decay of correlations and other properties.

Findings

Decay of correlation established

Analyticity of free energy proven

Central limit theorem demonstrated

Abstract

We use the Hilbert distance on cones and the Birkhoff-Hopf Theorem to prove decay of correlation, analyticity of the free energy and a central limit theorem in the one dimensional Jellium model with non constant density charge background, both in the classical and quantum cases.